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A comparative study of the power-law relationship between the pulse width and energy of precursor and main burst 前体与主爆脉冲宽度与能量幂律关系的比较研究
4区 物理与天体物理 Q3 ASTRONOMY & ASTROPHYSICS Pub Date : 2023-10-18 DOI: 10.1088/1674-4527/ad0497
Hui-Ying Deng, Zhaoyang Peng, Jia-Ming Chen, Dan Zhu
Abstract In gamma-ray burst (GRB) prompt emission, there is still no consistent conclusion if the precursor and the main burst share the same origin. In this paper, we try to study the issue based on the relationship between pulse width and energy of the precursor and main burst. We systematically search the light curve data observed by Swift/BAT and Fermi/GBM, and find 13 long bursts with well-structured precursors and main bursts. After fitting the precursor light curve of each different energy channel with the Norris function, we find that there is not only a power-law relationship between precursor width and energy, but also a power-law relationship between the ratio of the rising width to the decaying width and energy. By comparing the relationship between the precursors and the main burst pulses, we find that the distribution of the precursors and the relationship between the power law indices are roughly the same as those of the main burst. In addition, it is found that the precursor width distribution as well as the upper limit of the pulse width ratio do not exceed 1 and are asymmetric, which is also consistent with the main burst. These indicate that the precursor and the main burst are indistinguishable, and the precursor and the main burst may have the same physical origin.
在伽玛射线暴(GRB)瞬发中,前体和主暴是否来自同一起源,目前还没有一致的结论。本文试图从脉冲宽度与脉冲能量的关系出发,对脉冲宽度与脉冲能量的关系进行研究。我们系统地检索了Swift/BAT和Fermi/GBM观测到的光曲线数据,发现了13个具有结构良好的前体和主爆发的长爆发。利用Norris函数拟合各不同能量通道的前驱体光曲线,发现前驱体宽度与能量之间不仅存在幂律关系,而且上升宽度与衰减宽度之比与能量之间也存在幂律关系。通过对比前驱体与主爆脉冲的关系,我们发现前驱体的分布和幂律指标之间的关系与主爆大致相同。此外,发现前驱体宽度分布和脉宽比上限不超过1且不对称,这也与主爆发相一致。说明前驱体与主爆发难以区分,前驱体与主爆发可能具有相同的物理成因。
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引用次数: 0
Understanding the predication mechanism of deep learning through error propagation among parameters in strong lensing case 强透镜情况下参数间误差传播的深度学习预测机制研究
4区 物理与天体物理 Q3 ASTRONOMY & ASTROPHYSICS Pub Date : 2023-10-18 DOI: 10.1088/1674-4527/ad0498
Xi-Long Fan, Peizheng Wang, Jin Li, Nan Yang
Abstract The error propagation among estimated parameters reflects the correlation among the parameters. We study the capability of machine learning of ``learning" the correlation of estimated parameters. We show that machine learning can recover the relation between the uncertainties of different parameters, especially, as predicted by the error propagation formula. As a proof-of-principle test, a toy model of linear relation with Gaussian noise is presented. We found that the predictions obtained by machine learning indeed indicate the information about the law of error propagation and the distribution of noise. Gravitational lensing can be used to probe both astrophysics and cosmology. As a practical application, we show that the machine learning is able to intelligently find the error propagation among the gravitational lens parameters (effective lens mass $M_{L}$ and Einstein radius $theta_{E}$) in accordance with the theoretical formula for the singular isothermal ellipse (SIE) lens model. The relation of errors of lens mass and Einstein radius, (e.g. the ratio of standard deviations $mathcal{F}=sigma_{hat{ M_{L}}}/ sigma_{hat{theta_{E}}}$) predicted by the deep convolution neural network are consistent with the error propagation formula of SIE lens model. Error propagation plays a crucial role in identifying the physical relation among parameters, rather than a coincidence relation, therefore we anticipate our case study on the error propagation of machine learning predictions could extend to other physical systems on searching the correlation among parameters.
估计参数之间的误差传播反映了参数之间的相关性。我们研究了机器学习的能力,即“学习”估计参数的相关性。我们证明了机器学习可以恢复不同参数的不确定性之间的关系,特别是根据误差传播公式预测的。作为原理验证,本文给出了一个与高斯噪声线性关系的玩具模型。我们发现,通过机器学习获得的预测确实表明了有关误差传播规律和噪声分布的信息。引力透镜可以用来探测天体物理学和宇宙学。作为实际应用,我们证明了机器学习能够根据奇异等温椭圆(SIE)透镜模型的理论公式智能地找到引力透镜参数(有效透镜质量$M_{L}$和爱因斯坦半径$theta_{E}$)之间的误差传播。深度卷积神经网络预测的透镜质量误差与爱因斯坦半径的关系(如标准差比$mathcal{F}=sigma_{hat{ M_{L}}}/ sigma_{hat{theta_{E}}}$)与SIE透镜模型的误差传播公式一致。误差传播在识别参数之间的物理关系而不是巧合关系中起着至关重要的作用,因此我们期望我们对机器学习预测的误差传播的案例研究可以扩展到其他物理系统中搜索参数之间的相关性。
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引用次数: 0
PyMsOfa: A Python Package for the Standards of Fundamental Astronomy (SOFA) Service 基础天文学标准(SOFA)服务的Python包
4区 物理与天体物理 Q3 ASTRONOMY & ASTROPHYSICS Pub Date : 2023-10-18 DOI: 10.1088/1674-4527/ad0499
Jianghui Ji, Dongjie Tan, Chunhui Bao, Xiumin Huang, Shoucun HU, Yao Dong, Su Wang
Abstract The Standards of Fundamental Astronomy (SOFA) is a service provided by the International Astronomical Union (IAU) that offers algorithms and software for astronomical calculations, which was released in two versions by FORTRAN 77 and ANSI C, respectively. textbf{In this work, we implement the python package PyMsOfa for SOFA service by three ways: (1) a python wrapper package based on a foreign function library for Python (ctypes), (2) a python wrapper package with the foreign function interface for Python calling C code (cffi), and (3) a python package directly written in pure python codes from SOFA subroutines.} The package PyMsOfa has fully implemented 247 functions of the original SOFA routines. In addition, PyMsOfa is also extensively examined, which is exactly consistent with those test examples given by the original SOFA. This python package can be suitable to not only the astrometric detection of habitable planets of the Closeby Habitable Exoplanet Survey (CHES) mission citep{ji2022ches}, but also for the frontiers themes of black holes and dark matter related to astrometric calculations and other fields. The source codes are available via https://github.com/CHES2023/PyMsOfa.
基础天文学标准(SOFA)是国际天文学联合会(IAU)提供的天文计算算法和软件服务,分别以FORTRAN 77和ANSI C语言发布了两个版本。textbf{在这项工作中,我们通过三种方式实现了用于SOFA服务的python包PyMsOfa:(1)基于python外部函数库的python包装器包(ctypes),(2)带有python调用C代码的外部函数接口的python包装器包(cffi),以及(3)直接用来自SOFA子程序的纯python代码编写的python包。}包PyMsOfa完全实现了原始SOFA例程的247个功能。此外,还对PyMsOfa进行了广泛的检查,这与原SOFA给出的测试示例完全一致。该python包不仅可以适用于近距离宜居系外行星调查(CHES)任务(citep{ji2022ches})中可居住行星的天体测量探测,还可以适用于与天体测量计算相关的黑洞和暗物质等前沿主题。源代码可通过https://github.com/CHES2023/PyMsOfa获得。
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引用次数: 0
New continuum observations of the Andromeda galaxy M 31 with FAST 用FAST对仙女座星系m31的新连续观测
4区 物理与天体物理 Q3 ASTRONOMY & ASTROPHYSICS Pub Date : 2023-10-17 DOI: 10.1088/1674-4527/acfae1
wenjun Zhang, Xiaohui Sun, Jie Wang
Abstract We present a new total intensity image of M31 at 1.248 GHz, observed with the Five-hundred-meter Aperture Spherical radio telescope (FAST) with an angular resolution of 4 and a sensitivity of about 16 mK. The new FAST image clearly reveals weak emission outside the ring due to its high sensitivity on large-scale structures. We derive a scale length of 2.7 kpc for the cosmic ray electrons and find that the cosmic ray electrons propagate mainly through diffusion by comparing the scale length at 4.8 GHz. The spectral index of the total intensity varies along the ring, which can be attributed to the variation of the spectra of synchrotron emission. This variation is likely caused by the change of star formation rates along the ring. We find that the azimuthal profile of the non-thermal emission can be interpreted by an axisymmetric large-scale magnetic field with varying pitch angle along the ring, indicating a complicated magnetic field configuration in M31.
摘要利用角分辨率为4’、灵敏度约为16 mK的500米口径球面射电望远镜(FAST)在1.248 GHz观测到M31的新总强度图像。由于FAST对大尺度结构的高灵敏度,新的FAST图像清晰地显示了环外的弱发射。我们推导出宇宙射线电子的尺度长度为2.7 kpc,并通过比较4.8 GHz的尺度长度发现宇宙射线电子主要通过扩散传播。总强度的光谱指数沿环形变化,这可归因于同步辐射光谱的变化。这种变化很可能是由环上恒星形成速率的变化引起的。研究发现,非热发射的方位角剖面可以用沿环方向变化的轴对称大尺度磁场来解释,表明M31具有复杂的磁场构型。
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引用次数: 0
GRB 220408B: A Three-Episode Burst from a Precessing Jet GRB 220408B:一个三集的喷气机爆发
4区 物理与天体物理 Q3 ASTRONOMY & ASTROPHYSICS Pub Date : 2023-10-17 DOI: 10.1088/1674-4527/acfa59
Zijian Zhang, Yi-Han Iris Yin, Chenyu Wang, Xiangyu Ivy Wang, Jun Yang, Yan-Zhi Meng, Zi-Ke Liu, Guo-Yin Chen, Xiaoping Fu, Huaizhong Gao, Sihao Li, Yihui Liu, Xiangyun Long, Yong-Chang Ma, Xiaofan Pan, Yuanze Sun, Wei Wu, Zirui Yang, Zhizhen Ye, Xiaoyu Yu, Shuheng Zhao, Xutao Zheng, Tao Zhou, Qing-Wen Tang, Qiurong Qiu, Rong Zhou, Zhonghai Wang, Hua Feng, Ming Zeng, Binbin Zhang
Abstract Jet precession has previously been proposed to explain the apparently repeating features in the light curves of a few gamma-ray bursts (GRBs). In this paper, we further apply the precession model to a bright GRB 220408B by examining both its temporal and spectral consistency with the predictions of the model. As one of the recently confirmed GRBs observed by our GRID CubeSat mission, GRB 220408B is noteworthy as it exhibits three apparently similar emission episodes. Furthermore, the similarities are reinforced by their strong temporal correlations and similar features in terms of spectral evolution and spectral lags. Our analysis demonstrates that these features can be well explained by the modulated emission of a Fast-Rise-Exponential-Decay (FRED) shape light curve intrinsically produced by a precessing jet with a precession period of 18.4 0.2 + 0.2 s, a nutation period of 11.1 0.2 + 0.2 s and viewed off-axis. This study provides a straightforward explanation for the complex yet similar multi-episode GRB light curves.
射流进动先前被提出用来解释一些伽马射线暴(GRBs)的光曲线中明显重复的特征。在本文中,我们进一步将进动模型应用于明亮的GRB 220408B,通过检验其时间和光谱与模型预测的一致性。GRB 220408B是我们的GRID立方体卫星任务最近观测到的确认的GRB之一,值得注意的是,它表现出三次明显相似的发射事件。此外,它们在光谱演化和光谱滞后方面的强时间相关性和相似特征增强了相似性。我们的分析表明,这些特征可以很好地解释为快速上升-指数衰减(FRED)形状光曲线的调制发射,该光曲线本质上是由进动周期为18.4−0.2 + 0.2 s的进动射流产生的,章动周期为11.1−0.2 + 0.2 s,并且离轴观察。这项研究为复杂而相似的GRB光曲线提供了一个直接的解释。
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引用次数: 0
The possibility of detecting our solar system through astrometry 通过天体测量探测太阳系的可能性
4区 物理与天体物理 Q3 ASTRONOMY & ASTROPHYSICS Pub Date : 2023-10-17 DOI: 10.1088/1674-4527/acfc9b
Donghong Wu
Abstract Searching for exoplanets with different methods has always been the focus of astronomers over the past few years. Among multiple planet detection techniques, astrometry stands out for its capability to accurately determine the orbital parameters of exoplanets. In this study, we examine the likelihood of extraterrestrial intelligent civilizations detecting planets in our solar system using the astrometry method. By conducting injection-recovery simulations, we investigate the detectability of the four giant planets in our solar system under different observing baselines and observational errors. Our findings indicate that extraterrestrial intelligence could detect and characterize all four giant planets, provided they are observed for a minimum of 90 yr with signal-noise ratios exceeding 1. For individual planets such as Jupiter, Saturn, and Neptune, a baseline that surpasses half of their orbital periods is necessary for detection. However, Uranus requires longer observing baselines since its orbital period is roughly half of that of Neptune. If the astrometry precision is equal to or better than 10 μ as, all 8707 stars located within 30 pc of our solar system possess the potential to detect the four giant planets within 100 yr. Additionally, our prediction suggests that over 300 stars positioned within 10 pc from our solar system could detect our Earth if they achieve an astrometry precision of 0.3 μ as.
在过去的几年里,用不同的方法寻找系外行星一直是天文学家关注的焦点。在多行星探测技术中,天体测量以其精确确定系外行星轨道参数的能力而脱颖而出。在这项研究中,我们研究了外星智能文明探测我们太阳系行星的可能性,使用天体测量方法。通过注入-回收模拟,研究了在不同观测基线和观测误差下,太阳系四颗巨行星的可探测性。我们的研究结果表明,只要对这四颗巨行星进行至少90年的观测,并且信噪比超过1,地外智慧生物就可以探测到并描述它们的特征。对于单个行星,如木星、土星和海王星,探测需要超过其轨道周期一半的基线。然而,天王星需要更长的观测基线,因为它的轨道周期大约是海王星的一半。如果天体测量精度等于或高于10 μ as,那么位于太阳系30%以内的8707颗恒星都有可能在100年内探测到这四颗巨行星。此外,我们的预测表明,位于太阳系10%以内的300多颗恒星如果达到0.3 μ as的天体测量精度,就可以探测到我们的地球。
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引用次数: 0
Distributed Control Software for the Active Surface System of Tian-ma Radio telescope 天马射电望远镜主动地面系统分布式控制软件
4区 物理与天体物理 Q3 ASTRONOMY & ASTROPHYSICS Pub Date : 2023-10-17 DOI: 10.1088/1674-4527/acfa58
dong Zhang, Rongbing Zhao, Zhen Yan, WeiHua ShangGuan, Qian Ye, Zhiqiang Shen, Qinghui Liu, jinqing Wang, Li Fu, Chu-Yuan Zhang, Dong-fang Song, Si-Yu Liu
Abstract The Tian-ma Radio Telescope (TMRT) applies an Active Surface System (ASFS), which corrects for large-scale deformations due to gravity and thermal on the primary reflector. The centralized and automated management of the ASFS using software has become a challenge, for which we have developed the TMRT Active Surface System Control Software (TASCS). This paper describes the design and implementation of TASCS for device control, status monitoring, human-computer interaction, and data management functionalities. TASCS adopts the open-source Tango Controls framework and distributes middleware technology to realize real-time automated adjustment of the primary reflector through remote centralized control of a large number of actuators. At present, it has been successfully deployed on the TMRT and has played an important role in Event Horizon Telescope observations.
摘要:天马射电望远镜(TMRT)采用主动表面系统(ASFS),对主反射镜上由于重力和热引起的大规模变形进行校正。利用软件对ASFS进行集中和自动化管理已成为一个挑战,为此我们开发了TMRT主动地面系统控制软件(TASCS)。本文描述了TASCS在设备控制、状态监控、人机交互和数据管理等方面的设计与实现。TASCS采用开源的Tango Controls框架和分布式中间件技术,通过远程集中控制大量执行器,实现主反射镜的实时自动调节。目前,它已成功部署在TMRT上,并在事件视界望远镜观测中发挥了重要作用。
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引用次数: 0
Research on UWL signal channelization for Xinjiang 110 m radio telescope 新疆110 m射电望远镜UWL信号信道化研究
4区 物理与天体物理 Q3 ASTRONOMY & ASTROPHYSICS Pub Date : 2023-10-17 DOI: 10.1088/1674-4527/ad0427
hailong zhang, Zhang Yazhou, Meng ZHANG, Jie WANG, Jian Li, Xinchen YE, Xin Pei
Abstract Aiming at the subband division of UWL (Ultra-Wide wideband Low-frequency) signal (frequency coverage range :704-4032 MHz) of Xinjiang 110 m radio telescope (QTT), a scheme of ultra-wide bandwidth signal is designed. Firstly, we analyze the effect of different window functions such as Hanning window, Hamming window and Kaiser window on the performance of FIR (Finite Impulse Response) digital filters, and implement a CS-PFB (Critical Sampling Polyphase Filter Bank) based on the Hamming window FIR digital filter. Secondly, we generate 3328 MHz simulation data of ultra-wideband pulsar baseband in the frequency range of 704-4032 MHz using the UBPB (Ultra-wide Bandwitdh Pulsar Baseband data generation) algorithm based on the 400 MHz bandwidth pulsar baseband data obtained from Parkes CASPSR observations. Thirdly, we obtain 26 subbands of 128 MHz based on CS-PFB and the simulation data, and the pulse profile of each subband by coherent dispersion, integration, and folding. Finally, the phase of each subband pulse profile is aligned by non-coherent dedispersion, and to generate a broadband pulse profile, which is basically the same as the pulse profile obtained from the original data using DSPSR. The experimental results show that the scheme of QTT UWL reception system is feasible, and the proposed channel algorithm in this paper is effective.
针对新疆110 m射电望远镜(QTT) UWL (Ultra-Wide wideb低频)信号(频率覆盖范围:704-4032 MHz)的子带划分问题,设计了一种超宽带信号方案。首先,我们分析了不同窗函数如Hanning窗、Hamming窗和Kaiser窗对FIR (Finite Impulse Response)数字滤波器性能的影响,并基于Hamming窗FIR数字滤波器实现了CS-PFB (Critical Sampling多相滤波器组)。其次,基于Parkes CASPSR观测得到的400 MHz带宽脉冲星基带数据,采用UBPB (Ultra-wide bandbandwidth pulsar baseband data generation)算法生成704 ~ 4032 MHz频率范围内的3328 MHz超宽带脉冲星基带模拟数据。第三,基于CS-PFB和仿真数据得到了128 MHz的26个子带,并通过相干色散、积分和折叠得到了每个子带的脉冲轮廓;最后,通过非相干去色散对各子带脉冲剖面的相位进行对准,得到与DSPSR原始数据得到的脉冲剖面基本相同的宽带脉冲剖面。实验结果表明,QTT UWL接收系统方案是可行的,本文提出的信道算法是有效的。
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引用次数: 0
Early phases of star formation: testing chemical tools 恒星形成的早期阶段:测试化学工具
4区 物理与天体物理 Q3 ASTRONOMY & ASTROPHYSICS Pub Date : 2023-10-17 DOI: 10.1088/1674-4527/ad0429
Sergio Paron
Abstract The star forming processes strongly influence the ISM chemistry. &#xD;Nowadays, there are available many high-quality databases at millimeter wavelengths. Using them, it is possible to carry out studies that review and deepen previous results. If these studies involve large samples of sources, it is preferred to use {bf direct} tools to study the molecular gas.&#xD;With the aim of testing these tools such as the use of the HCN/HNC ratio as a thermometer, and the use of H$^{13}$CO$^{+}$, HC$_{3}$N, N$_{2}$H$^{+}$, and C$_{2}$H as ``chemical clocks'', we present a molecular line study towards 55 sources representing {bf massive young stellar objects (MYSOs)} at different evolutive stages: infrared dark clouds (IRDCs), high-mass protostellar objects (HMPOs), hot molecular cores (HMCs) and {bf ultracompact hii~regions (UChii)}.&#xD;We found that the use of HCN/HNC ratio as an universal thermometer in the ISM should be taken with care because the HCN optical depth is a big issue that can affect the method. Hence, this tool should be used only after a careful analysis of the HCN spectrum, checking that no line, neither the main nor the hyperfine ones, present absorption features.&#xD;We point out that the analysis of the emission of H$^{13}$CO$^{+}$, HC$_{3}$N, N$_{2}$H$^{+}$, and C$_{2}$H could be useful to trace and distinguish regions among IRDCs, HMPOs and HMCs. &#xD;The molecular line widths of these four species increase from the IRDC to the HMC stage, which can be a consequence of the gas dynamics related to the star-forming processes taking place in the molecular clumps. &#xD;Our results do not only contribute with more statistics regarding to probe such chemical tools, useful to obtain information in large samples of sources, but also complement previous works through the analysis on other types of sources.
恒星形成过程对ISM化学有很大影响。如今,有许多高质量的毫米波数据库可用。利用它们,可以进行研究,审查和深化以前的结果。如果这些研究涉及大量的源样本,最好使用{bf直接}工具来研究分子气体。 为了测试这些工具,如使用HCN/HNC比率作为温度计,使用H$^{13}$CO$^{+}$, HC$ $ {3}$N, N$ $ {2}$H$^{+}$和C$ $ {2}$H作为“化学时钟”,我们提出了代表{bf大质量年轻恒星天体(MYSOs)}的55个源的分子线研究。红外暗云(IRDCs)、高质量原恒星天体(HMPOs)、热分子核(HMCs)和{bf超压缩hii~区域(UChii)}.我们发现,在ISM中使用HCN/HNC比值作为通用温度计应该谨慎,因为HCN光学深度是影响方法的一个大问题。因此,只有对HCN光谱进行仔细的分析,检查主谱线和超细谱线都没有吸收特征。 。我们指出,对H$^{13}$CO$^{+}$、HC$ $ {3}$N、N$ $ {2}$H$ $^{+}$和C$ $ {2}$H的发射分析可以用来追踪和区分irdc、HMPOs和hmc之间的区域。从IRDC到HMC阶段,这四种物质的分子线宽度增加,这可能是与分子团块中发生的恒星形成过程相关的气体动力学的结果。我们的结果不仅有助于提供更多关于探测这类化学工具的统计数据,有助于在大量来源样本中获取信息,而且还通过对其他类型来源的分析补充了以前的工作。
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引用次数: 0
Studying the Equilibrium Points of the Modified Circular Restricted Three-Body Problem: the Case of Sun-Haumea System 修正圆形受限三体问题的平衡点研究——以太阳-妊星系统为例
4区 物理与天体物理 Q3 ASTRONOMY & ASTROPHYSICS Pub Date : 2023-10-17 DOI: 10.1088/1674-4527/acf978
Ibnu Nurul Huda, Budi Dermawan, Muhammad Bayu Saputra, Rifki Sadikin, Taufiq Hidayat
We intend to study a modified version of the planar Circular Restricted Three-Body Problem (CRTBP) by incorporating several perturbing parameters. We consider the bigger primary as an oblate spheroid and emitting radiation while the small primary has an elongated body. We also consider the perturbation from a disk-like structure encompassing this three-body system. First, we develop a mathematical model of this modified CRTBP. We have found there exist five equilibrium points in this modified CRTBP model, where three of them are collinear and the other two are non-collinear. Second, we apply our modified CRTBP model to the Sun-Haumea system by considering several values of each perturbing parameter. Through our numerical investigation, we have discovered that the incorporation of perturbing parameters has resulted in a shift in the equilibrium point positions of the Sun-Haumea system compared to their positions in the classical CRTBP. The stability of equilibrium points is investigated. We have shown that the collinear equilibrium points are unstable and the stability of non-collinear equilibrium points depends on the mass parameter $mu$ of the system. Unlike the classical case, non-collinear equilibrium points have both a maximum and minimum limit of $mu$ for achieving stability. We remark that the stability range of $mu$ in non-collinear equilibrium points depends on the perturbing parameters. In context of the Sun-Haumea system, we have found that the non-collinear equilibrium points are stable.
我们打算研究平面圆形受限三体问题(CRTBP)的一个改进版本,该问题包含了几个扰动参数。我们认为较大的初生星是一个扁球体并发射辐射,而较小的初生星有一个细长的体。我们还考虑了围绕这个三体系统的盘状结构的摄动。首先,我们建立了改进后的CRTBP的数学模型。我们发现在修正的CRTBP模型中存在5个平衡点,其中3个共线,另外2个非共线。其次,我们将改进的CRTBP模型应用于太阳-妊神星系统,考虑每个扰动参数的几个值。通过我们的数值研究,我们发现,与经典的CRTBP相比,摄动参数的加入导致太阳-妊神星系统的平衡点位置发生了变化。研究了平衡点的稳定性。我们已经证明了共线平衡点是不稳定的,非共线平衡点的稳定性取决于系统的质量参数$mu$。与经典情况不同,非共线平衡点具有达到稳定性的最大和最小极限$mu$。我们注意到$mu$在非共线平衡点上的稳定范围取决于摄动参数。在太阳-妊神星系统中,我们发现其非共线平衡点是稳定的。
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引用次数: 0
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Research in Astronomy and Astrophysics
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